We analyze existence of equilibrium in a one-dimensional model of endogenous party platforms and more than two parties. The platforms proposed by parties depend on their membership composition. The policy implemented is a function of the different proposals and the vote distribution among such proposals. It is shown that if voters are sincere there is always an equilibrium
regardless of the number of parties. In the case of strategic voting behavior, existence of equilibrium can be shown provided a subadditivity condition on the outcome function holds.